FVAdvection

Residual contribution from advection operator for finite volume method.

The FVAdvection kernel implements an advection term given for the domain ( $var element = document.getElementById("moose-equation-73c27f6a-25af-43c6-a8bf-e778fed9670f");katex.render("\\Omega", element, {displayMode:false,throwOnError:false});$ ) defined as

var element = document.getElementById("moose-equation-e9857396-ef57-4d08-9404-3cc6d4b24c4d");katex.render("\\underbrace{\\vec{v} \\cdot \\nabla u} + \\sum_{i=1}^n \\beta_i = 0 \\in \\Omega,", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-8fa4c9c7-f14d-442a-8e4e-ce7911bc5c6b");katex.render("u", element, {displayMode:false,throwOnError:false});$ is the advected quantity, the variable for this kernel, $var element = document.getElementById("moose-equation-bdd8a298-027d-4505-9f99-cc59f621837f");katex.render("v", element, {displayMode:false,throwOnError:false});$ is the constant advecting velocity, the velocity parameter of this kernel, and the $var element = document.getElementById("moose-equation-bf88537d-1d7c-4e29-bd1a-13201b85b005");katex.render("\\beta_i", element, {displayMode:false,throwOnError:false});$ are the contribution to the residual of other kernels.

This volumetric term is transformed using the divergence theorem into a surface integral, computed as a sum over each face of the advective flux. This is preferred over computing a volumetric gradient as conservative advection is naturally achieved.

var element = document.getElementById("moose-equation-ad63a1f2-d21f-4174-a8eb-af5e06749fa3");katex.render("\\int_{element} \\vec{v} \\cdot \\nabla u = \\sum_{elem faces f} u_f \\vec{v} \\cdot n_f v area_f", element, {displayMode:true,throwOnError:false});

The advected quantity is evaluated on the face using an advected_interp(olation)_method. Two methods are available:

average for a geometrically weighted average between the element and neighbor values
upwind for a first order upwind scheme, which uses the value from the centroid of the element situated upwind of the face, using velocity as the wind

note

This kernel leverages the automatic differentiation system, so the Jacobian is computed at the same time as the residual and need not be defined separately.

Boundary conditions for pure advection

Advection problems, with a constant advecting velocity, should have two types of boundary conditions: inflow and outflow. The inflow boundary conditions may be specified as a constant boundary value with a FVDirichletBC (with caveats, see documentation)

[FVBCs]
  [left]
    type = FVFunctionDirichletBC
    boundary = 'left'
    function = 'exact'
    variable = v
  []
[]

The outflow boundary conditions may be specified with a FVConstantScalarOutflowBC.

[FVBCs]
  [fv_outflow]
    type = FVConstantScalarOutflowBC
    velocity = '1 0.5 0'
    variable = v
    boundary = 'right top'
  []
[]

If no boundary conditions are specified, then there is a zero advective flux through the boundary, also known a no-penetration boundary condition.

note

The FVAdvection kernel may be executed on boundaries using the force_boundary_execution and boundaries_to_force parameters, however this is somewhat situational / not for mainstream use.

Example input syntax

In this example, a simple time-dependent advection problem is solved, with a constant advecting velocity of 1 0.5 0.

[FVKernels]
  [advection]
    type = FVAdvection
    variable = v
    velocity = '1 0.5 0'
  []
  [time]
    type = FVTimeKernel
    variable = v
  []
[]

Input Parameters

variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Controllable:No
Description:The name of the variable that this residual object operates on
velocityConstant advection velocity
C++ Type:libMesh::VectorValue<double>
Controllable:No
Description:Constant advection velocity

Required Parameters

advected_interp_methodupwindThe interpolation to use for the advected quantity. Options are 'upwind', 'average', 'sou' (for second-order upwind), 'min_mod', 'vanLeer', 'quick', and 'skewness-corrected' with the default being 'upwind'.
Default:upwind
C++ Type:MooseEnum
Options:average, upwind, sou, min_mod, vanLeer, quick, skewness-corrected
Controllable:No
Description:The interpolation to use for the advected quantity. Options are 'upwind', 'average', 'sou' (for second-order upwind), 'min_mod', 'vanLeer', 'quick', and 'skewness-corrected' with the default being 'upwind'.
blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

boundaries_to_avoidThe set of sidesets to not execute this FVFluxKernel on. This takes precedence over force_boundary_execution to restrict to less external boundaries. By default flux kernels are executed on all internal boundaries and Dirichlet boundary conditions.
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The set of sidesets to not execute this FVFluxKernel on. This takes precedence over force_boundary_execution to restrict to less external boundaries. By default flux kernels are executed on all internal boundaries and Dirichlet boundary conditions.
boundaries_to_forceThe set of sidesets to force execution of this FVFluxKernel on. Setting force_boundary_execution to true is equivalent to listing all external mesh boundaries in this parameter.
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The set of sidesets to force execution of this FVFluxKernel on. Setting force_boundary_execution to true is equivalent to listing all external mesh boundaries in this parameter.
force_boundary_executionFalseWhether to force execution of this object on all external boundaries.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to force execution of this object on all external boundaries.

Boundary Execution Modification Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

ghost_layers1The number of layers of elements to ghost.
Default:1
C++ Type:unsigned short
Controllable:No
Description:The number of layers of elements to ghost.
use_point_neighborsFalseWhether to use point neighbors, which introduces additional ghosting to that used for simple face neighbors.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to use point neighbors, which introduces additional ghosting to that used for simple face neighbors.

Parallel Ghosting Parameters

(moose/test/tests/fvkernels/mms/advective-outflow/advection-diffusion.i)

diff=1
a=1

[GlobalParams]
  advected_interp_method = 'average'
[]

[Mesh]
  [./gen_mesh]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = -1
    xmax = 0
    nx = 2
  [../]
[]

[Variables]
  [./v]
    family = MONOMIAL
    order = CONSTANT
    fv = true
  [../]
[]

[FVKernels]
  [./advection]
    type = FVAdvection
    variable = v
    velocity = '${a} 0 0'
    force_boundary_execution = true
  [../]
  [./diffusion]
    type = FVDiffusion
    variable = v
    coeff = coeff
  [../]
  [body_v]
    type = FVBodyForce
    variable = v
    function = 'forcing'
  []
[]

[FVBCs]
  [left]
    type = FVFunctionDirichletBC
    boundary = 'left'
    function = 'exact'
    variable = v
  []
[]

[Materials]
  [diff]
    type = ADGenericFunctorMaterial
    prop_names = 'coeff'
    prop_values = '${diff}'
  []
[]

[Functions]
  [exact]
    type = ParsedFunction
    expression = 'cos(x)'
  []
  [forcing]
    type = ParsedFunction
    expression = 'cos(x) - sin(x)'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
[]

[Outputs]
  exodus = true
  csv = true
[]

[Postprocessors]
  [./error]
    type = ElementL2Error
    variable = v
    function = exact
    outputs = 'console csv'
    execute_on = 'timestep_end'
  [../]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(moose/test/tests/fvkernels/fv_constant_scalar_advection/2D_constant_scalar_advection.i)

[Mesh]
  [gen_mesh]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 4
    nx = 10
    ny = 20
  []
[]

[Variables]
  [v]
    type = MooseVariableFVReal
    two_term_boundary_expansion = false
  []
[]

[ICs]
  [v_ic]
    type = FunctionIC
    variable = v
    function = 'r2 := (x - 0.5)*(x - 0.5) + (y - 0.3)*(y - 0.3); exp(-r2 * 20)'
  []
[]

[FVKernels]
  [advection]
    type = FVAdvection
    variable = v
    velocity = '1 0.5 0'
  []
  [time]
    type = FVTimeKernel
    variable = v
  []
[]

[FVBCs]
  [fv_outflow]
    type = FVConstantScalarOutflowBC
    velocity = '1 0.5 0'
    variable = v
    boundary = 'right top'
  []
[]

[Executioner]
  type = Transient
  petsc_options = '-snes_converged_reason'
  num_steps = 10
  dt = 0.25
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

(moose/test/tests/fvkernels/fv_constant_scalar_advection/2D_constant_scalar_advection.i)

[Mesh]
  [gen_mesh]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 4
    nx = 10
    ny = 20
  []
[]

[Variables]
  [v]
    type = MooseVariableFVReal
    two_term_boundary_expansion = false
  []
[]

[ICs]
  [v_ic]
    type = FunctionIC
    variable = v
    function = 'r2 := (x - 0.5)*(x - 0.5) + (y - 0.3)*(y - 0.3); exp(-r2 * 20)'
  []
[]

[FVKernels]
  [advection]
    type = FVAdvection
    variable = v
    velocity = '1 0.5 0'
  []
  [time]
    type = FVTimeKernel
    variable = v
  []
[]

[FVBCs]
  [fv_outflow]
    type = FVConstantScalarOutflowBC
    velocity = '1 0.5 0'
    variable = v
    boundary = 'right top'
  []
[]

[Executioner]
  type = Transient
  petsc_options = '-snes_converged_reason'
  num_steps = 10
  dt = 0.25
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]